Onset of convection in fluids with strongly temperature-dependent, power-law viscosity: 2. Dependence on the initial perturbation

The onset of convection in the power-law creep regime on the silicate and icy planetary bodies requires a finite amplitude initial perturbation. This is a nonlinear problem and thus, both the amplitude and shape of the perturbation are important. We performed numerical simulations of the onset of convection in a two-dimensional layer with a fixed temperature contrast between the boundaries and in the stagnant lid regime of temperature-dependent viscosity convection. The optimal perturbations are located at the bottom of the layer (in the rheological sublayer) and have the wavelength of about twice the thickness of the rheological sublayer. The critical Rayleigh number for the onset of convection by optimal perturbations is calculated for a broad range of viscosity parameters. The results are summarized in terms of simple scaling relationships.